A general construction of linear differential equations with solutions of prescribed properties

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Abstract

Effective constructions of ordinary linear differential equations of arbitrary orders are presented that give equations with solutions of prescribed qualitative properties, like solutions in the classes Lp, converging to zero or bounded solutions, etc. Connections with transformations of equations and distribution of the zeros of solutions are considered as well. Results generalize those obtained for the second-order linear differential equations.

Keywords

Construction of linear differential equations
Prescribed qualitative properties of solutions

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Research partially supported by Grants # 201/99/0295 of the Grant Agency, # A 101 99 02 of the Academy of Sciences of the Czech Republic and by the Department of Mathematics FEKT Tech. Univ. Brno.